Projects per year
My research interests lie in pure mathematics, and specifically in algebraic geometry and representation theory. Much of my research applies explicit methods to improve our understanding of moduli spaces of quiver representations and their derived categories.
One motivating question is to ask for nice moduli descriptions of well known varieties. This is now understood for projective toric varieties and, more generally, for Mori Dream Spaces. This leads naturally to the study of multigraded linear series (also known as framed quiver varieties or quiver flag varieties) as ambient spaces in noncommutative algebraic geometry.Another theme of my research is to understand which algebraic varieties carry tilting bundles, thereby providing an explicit understanding of their derived category of coherent sheaves. The first known examples were provided by Beilinson and Kapranov, while many of the more recent examples have been influenced by the McKay correspondence in one form or another. Examples include framed quiver varieties, G-Hilbert schemes, moduli spaces arising in the study of consistent dimer model algebras, and smooth toric Fano varieties in low dimensions. These constructions lead to interesting questions about mutation, wall crossing phenomena and Bridgeland stability manifolds.
Mathematics, Doctor of Science, The McKay correspondence and representations of the McKay quiver, University of Warwick
Award Date: 12 Jul 2001
- 1 Similar Profiles
Collaborations and top research areas from the last five years
Dive into details
Select a country/territory to view shared publications and projects
3/04/13 → 2/10/16
Project: Research council
Craw, A., Bellamy, G., Schedler, T., Rayan, S. & Weiss, H., 14 Nov 2023, (Acceptance date) In: Journal of Algebraic Geometry. 30 p.
Research output: Contribution to journal › Article › peer-review
Craw, A., 15 Nov 2021, (Acceptance date) The McKay correspondence, mutation and related topics.
Research output: Chapter or section in a book/report/conference proceeding › Chapter in a published conference proceeding
Craw, A., Heuberger, L. & Tapia Amador, J., 26 Feb 2021, In: Épijournal de Géométrie Algébrique. 5, 29 p., 4.
Research output: Contribution to journal › Article › peer-reviewOpen Access
Correction to: Geometric Reid’s recipe for dimer models (Mathematische Annalen, (2015), 361, 3-4, (689-723), 10.1007/s00208-014-1085-8)Bocklandt, R., Craw, A. & Quintero Vélez, A., 27 Jan 2021, In: Mathematische Annalen.
Research output: Contribution to journal › Comment/debate › peer-review
Craw, A., 20 Sept 2021, 23 p.
Research output: Working paper / Preprint › Preprint